arXiv research

Solves the film scheduling and staggered showtimes problem for movie theaters.

In this paper we first review the covering space method with constrained BV functions for solving the classical Plateau's problem. Next, we carefully analyze some interesting examples of soap films compatible with the covering space method: in particular, the case of a soap film only partially wetting a space curve, a …

Multi-layer optical film has been found to afford important applications in optical communication, optical absorbers, optical filters, etc. Different algorithms of multi-layer optical film design has been developed, as simplex method, colony algorithm, genetic algorithm. These algorithms rapidly promote the design and …

In this paper we provide the first examples of non-flat soap films proven to span tetrahedra. These are members of a continuous two parameter family of soap films with tetrahedral boundaries. Of particular interest is a two parameter subfamily where each spanning soap film has the property that two minimal surfaces mee…

Soap films collapse only if their bulk has negative pressure, forming convex shapes.

Derives equilibrium law for Plateau borders in wet soap films and foams.

Recent breakthroughs in computer vision and natural language processing have spurred interest in challenging multi-modal tasks such as visual question-answering and visual dialogue. For such tasks, one successful approach is to condition image-based convolutional network computation on language via Feature-wise Linear …

We introduce a general-purpose conditioning method for neural networks called FiLM: Feature-wise Linear Modulation. FiLM layers influence neural network computation via a simple, feature-wise affine transformation based on conditioning information. We show that FiLM layers are highly effective for visual reasoning - an…

Extends symmetry and rigidity to surfaces with soap film-like singularities.

We prove existence and a.e. regularity of an area minimizing soap film with a bound on energy spanning a given Jordan curve in R^3. The energy of a film is defined to be the sum of its surface area and the length of its singular branched set. The class of surfaces over which area is minimized includes images of disks, …

A soap film is actually a thin solid fluid bounded by two surfaces of opposite orientation. It is natural to model the film using one polyhedron for each side. Two problems are to get the polyhedra for both sides to be in the same place without canceling each other out and to model triple junctions without introducing …

Develops a geometric framework for soap film instabilities.

What are the possible shapes of various things and why? For instance, when a closed wire or a frame is dipped into a soap solution and is raised up from the solution, the surface spanning the wire is a soap film. What are the possible shapes of soap films and why? Or, for instance, why is DNA like a double spiral stair…

Smoothness of collapsed regions in soap films is proven, indicating wetted singularities.

Classifies soap film surfaces with vertical potentials.

For a given boundary set consisting of arcs and vertices, with two or more arcs meeting at each vertex, we treat the problem of estimating the area density of a soap film-like surface spanning the boundary.

This paper presents a new Graph Neural Network (GNN) type using feature-wise linear modulation (FiLM). Many standard GNN variants propagate information along the edges of a graph by computing "messages" based only on the representation of the source of each edge. In GNN-FiLM, the representation of the target node of an…

A deep learning algorithm designs low-cost SPP films.

FiLM improves deep learning for long-term time series forecasting.

Malaria is a life-threatening disease affecting millions. Microscopy-based assessment of thin blood films is a standard method to (i) determine malaria species and (ii) quantitate high-parasitemia infections. Full automation of malaria microscopy by machine learning (ML) is a challenging task because field-prepared sli…

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoi…

Plateau's soap film problem is to find a surface of least area spanning a given boundary. We begin with a compact orientable $(n-2)$-dimensional submanifold $M$ of $\R^n$. If $M$ is connected, we say a compact set $X$ "spans" $M$ if $X$ intersects every Jordan curve whose linking number with $M$ is 1. Picture a soap fi…

Improved continual learning method using variational inference and FiLM layers.

Let $M$ be an $n$-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant $-κ^2$. Using the cone total curvature $TC(Γ)$ of a graph $Γ$ which was introduced by Gulliver and Yamada Math. Z. 2006, we prove that the density at any point of a soap film-like…

Motivated by the study of the equilibrium equations for a soap film hanging from a wire frame, we prove a compactness theorem for surfaces with asymptotically vanishing mean curvature and fixed or converging boundaries. In particular, we obtain sufficient geometric conditions for the minimal surfaces spanned by a given…

New method finds all thin film structures from reflectometry data.

In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution …

This paper proves that classical minimal surfaces of arbitrary topological type with total boundary curvature at most 4πmust be smoothly embedded. Related results are proved for varifolds and for soap film surfaces.

Improved multi-user VoiceFilter-Lite model for speech recognition.

Langmuir-Blodgett films (LB-films) consist from few LB-monolayers which are high structured nanomaterials that are very promising materials for applications. We use a geometrical approach to describe structurization into LB-monolayers. Consequently, we develop on the 1-jet space J^1([0,\infty),R^2) the single-time Lagr…

New method schedules learning rate without stopping time, outperforming existing methods.

This paper proposes a method to select project schedules with the lowest risk.

Machine learning speeds up FLIM analysis in biomedical research.

Optimizes financial auditor schedules to reduce time and costs.

ScheduleFree+ improves large language model training without schedules or learning rates.

Cosine schedule is optimal for discrete diffusion models.

We derive a new model for pre-strained thin films, which consists of minimizing a biharmonic energy of deformations $v\in W^{2,2}$ satisfying the Monge-Ampère constraint $\det\nabla^2v = f$. We further discuss multiplicity properties of the minimizers of this model, in some special cases.

Optimal learning rate schedules derived for various tasks.

The paper optimizes interpolation schedules in generative models to improve sampling accuracy.

New method converts and optimizes sampling schedules for generative models.

The paper presents a multi-power law for predicting loss curves across different learning rate schedules.

This paper proposes a system-agnostic policy for dynamic scheduling.

Current clinical practice to monitor patients' health follows either regular or heuristic-based lab test (e.g. blood test) scheduling. Such practice not only gives rise to redundant measurements accruing cost, but may even lead to unnecessary patient discomfort. From the computational perspective, heuristic-based test …

More and more companies have deployed machine learning (ML) clusters, where deep learning (DL) models are trained for providing various AI-driven services. Efficient resource scheduling is essential for maximal utilization of expensive DL clusters. Existing cluster schedulers either are agnostic to ML workload characte…

Optimal learning rate schedules for SGD in changing data distributions.

Enhances multi-project scheduling with multiple priority rules.

Learning-rate schedules for large models match optimization theory closely, leading to better training.

The study introduces anytime learning schedules for large language models without fixed horizons.